Question

An observer and a source are each moving towards a point P in-between them. The observer is moving towards point P at a speed of 2m/s. The sound source of frequency 20Hz is moving towards point P with a speed of 10m/s. What will be the frequency as heard by the observer?

Answer 1

The observed frequency when a source is moving towards an observer can be calculated using the formula fo = fs (v + vo) / (v - vs), where fo is the observed frequency, fs is the source frequency, v is the speed of sound, vo is the observer's velocity, and vs is the source's velocity. In this case, the observed frequency is approximately 19.33Hz.

Step-by-step explanation:

The observed frequency when a source is moving towards an observer can be calculated using the formula:

fo = fs (v + vo) / (v - vs)

Where fo is the observed frequency, fs is the source frequency, v is the speed of sound, vo is the observer's velocity, and vs is the source's velocity. In this case, the source frequency is 20Hz, the speed of sound is 331m/s, the observer's velocity is -2m/s (since they are moving towards the point P), and the source's velocity is -10m/s (since it is also moving towards point P).

Plugging these values into the formula:

fo = 20Hz (331m/s + (-2m/s)) / (331m/s - (-10m/s))

Simplifying further:

fo = 20Hz (331m/s - 2m/s) / (331m/s + 10m/s)

Calculating:

`fo = 20Hz * (329m/s) / (341m/s)`

fo ≈ 19.33Hz